Nonlinear Pdes A Dynamical Systems Approach

Author : Guido Schneider
Publisher :
ISBN 13 : 9781470442286
Total Pages : 593 pages
Book Rating : 4.80/5 ( download)

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Download or read book Nonlinear PDEs written by Guido Schneider and published by . This book was released on 2017 with total page 593 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introductory textbook about nonlinear dynamics of PDEs, with a focus on problems over unbounded domains and modulation equations. The presentation is example-oriented, and new mathematical tools are developed step by step, giving insight into some important classes of nonlinear PDEs and nonlinear dynamics phenomena which may occur in PDEs. The book consists of four parts. Parts I and II are introductions to finite- and infinite-dimensional dynamics defined by ODEs and by PDEs over bounded domains, respectively, including the basics of bifurcation and attractor theory. Part III introduces PDEs on the real line, including the Korteweg-de Vries equation, the Nonlinear Schrödinger equation and the Ginzburg-Landau equation. These examples often occur as simplest possible models, namely as amplitude or modulation equations, for some real world phenomena such as nonlinear waves and pattern formation. Part IV explores in more detail the connections between such complicated physical systems and the reduced models. For many models, a mathematically rigorous justification by approximation results is given. The parts of the book are kept as self-contained as possible. The book is suitable for self-study, and there are various possibilities to build one- or two-semester courses from the book

Author : Guido Schneider
Publisher : American Mathematical Soc.
ISBN 13 : 1470436132
Total Pages : 575 pages
Book Rating : 4.31/5 ( download)

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Download or read book Nonlinear PDEs: A Dynamical Systems Approach written by Guido Schneider and published by American Mathematical Soc.. This book was released on 2017-10-26 with total page 575 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introductory textbook about nonlinear dynamics of PDEs, with a focus on problems over unbounded domains and modulation equations. The presentation is example-oriented, and new mathematical tools are developed step by step, giving insight into some important classes of nonlinear PDEs and nonlinear dynamics phenomena which may occur in PDEs. The book consists of four parts. Parts I and II are introductions to finite- and infinite-dimensional dynamics defined by ODEs and by PDEs over bounded domains, respectively, including the basics of bifurcation and attractor theory. Part III introduces PDEs on the real line, including the Korteweg-de Vries equation, the Nonlinear Schrödinger equation and the Ginzburg-Landau equation. These examples often occur as simplest possible models, namely as amplitude or modulation equations, for some real world phenomena such as nonlinear waves and pattern formation. Part IV explores in more detail the connections between such complicated physical systems and the reduced models. For many models, a mathematically rigorous justification by approximation results is given. The parts of the book are kept as self-contained as possible. The book is suitable for self-study, and there are various possibilities to build one- or two-semester courses from the book.

Author : Victor A. Galaktionov
Publisher : Springer Science & Business Media
ISBN 13 : 1461220505
Total Pages : 388 pages
Book Rating : 4.03/5 ( download)

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Download or read book A Stability Technique for Evolution Partial Differential Equations written by Victor A. Galaktionov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: * Introduces a state-of-the-art method for the study of the asymptotic behavior of solutions to evolution partial differential equations. * Written by established mathematicians at the forefront of their field, this blend of delicate analysis and broad application is ideal for a course or seminar in asymptotic analysis and nonlinear PDEs. * Well-organized text with detailed index and bibliography, suitable as a course text or reference volume.

Author : Christian Kuehn
Publisher : SIAM
ISBN 13 : 1611975662
Total Pages : 267 pages
Book Rating : 4.66/5 ( download)

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Download or read book PDE Dynamics written by Christian Kuehn and published by SIAM. This book was released on 2019-04-10 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an overview of the myriad methods for applying dynamical systems techniques to PDEs and highlights the impact of PDE methods on dynamical systems. Also included are many nonlinear evolution equations, which have been benchmark models across the sciences, and examples and techniques to strengthen preparation for research. PDE Dynamics: An Introduction is intended for senior undergraduate students, beginning graduate students, and researchers in applied mathematics, theoretical physics, and adjacent disciplines. Structured as a textbook or seminar reference, it can be used in courses titled Dynamics of PDEs, PDEs 2, Dynamical Systems 2, Evolution Equations, or Infinite-Dimensional Dynamics.

Author : Peter A. Cook
Publisher : Prentice Hall
ISBN 13 :
Total Pages : 234 pages
Book Rating : 4.30/5 ( download)

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Download or read book Nonlinear Dynamical Systems written by Peter A. Cook and published by Prentice Hall. This book was released on 1986 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Panagiotis D. Christofides
Publisher : Springer Science & Business Media
ISBN 13 : 1461201853
Total Pages : 262 pages
Book Rating : 4.54/5 ( download)

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Download or read book Nonlinear and Robust Control of PDE Systems written by Panagiotis D. Christofides and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: The interest in control of nonlinear partial differential equation (PDE) sys tems has been triggered by the need to achieve tight distributed control of transport-reaction processes that exhibit highly nonlinear behavior and strong spatial variations. Drawing from recent advances in dynamics of PDE systems and nonlinear control theory, control of nonlinear PDEs has evolved into a very active research area of systems and control. This book the first of its kind- presents general methods for the synthesis of nonlinear and robust feedback controllers for broad classes of nonlinear PDE sys tems and illustrates their applications to transport-reaction processes of industrial interest. Specifically, our attention focuses on quasi-linear hyperbolic and parabolic PDE systems for which the manipulated inputs and measured and controlled outputs are distributed in space and bounded. We use geometric and Lyapunov-based control techniques to synthesize nonlinear and robust controllers that use a finite number of measurement sensors and control actuators to achieve stabilization of the closed-loop system, output track ing, and attenuation of the effect of model uncertainty. The controllers are successfully applied to numerous convection-reaction and diffusion-reaction processes, including a rapid thermal chemical vapor deposition reactor and a Czochralski crystal growth process. The book includes comparisons of the proposed nonlinear and robust control methods with other approaches and discussions of practical implementation issues.

Author : Wassim M. Haddad
Publisher : Princeton University Press
ISBN 13 : 1400841046
Total Pages : 975 pages
Book Rating : 4.42/5 ( download)

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Download or read book Nonlinear Dynamical Systems and Control written by Wassim M. Haddad and published by Princeton University Press. This book was released on 2011-09-19 with total page 975 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Dynamical Systems and Control presents and develops an extensive treatment of stability analysis and control design of nonlinear dynamical systems, with an emphasis on Lyapunov-based methods. Dynamical system theory lies at the heart of mathematical sciences and engineering. The application of dynamical systems has crossed interdisciplinary boundaries from chemistry to biochemistry to chemical kinetics, from medicine to biology to population genetics, from economics to sociology to psychology, and from physics to mechanics to engineering. The increasingly complex nature of engineering systems requiring feedback control to obtain a desired system behavior also gives rise to dynamical systems. Wassim Haddad and VijaySekhar Chellaboina provide an exhaustive treatment of nonlinear systems theory and control using the highest standards of exposition and rigor. This graduate-level textbook goes well beyond standard treatments by developing Lyapunov stability theory, partial stability, boundedness, input-to-state stability, input-output stability, finite-time stability, semistability, stability of sets and periodic orbits, and stability theorems via vector Lyapunov functions. A complete and thorough treatment of dissipativity theory, absolute stability theory, stability of feedback systems, optimal control, disturbance rejection control, and robust control for nonlinear dynamical systems is also given. This book is an indispensable resource for applied mathematicians, dynamical systems theorists, control theorists, and engineers.

Author : Wassim M. Haddad
Publisher : Princeton University Press
ISBN 13 : 0691153469
Total Pages : 390 pages
Book Rating : 4.69/5 ( download)

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Download or read book Stability and Control of Large-Scale Dynamical Systems written by Wassim M. Haddad and published by Princeton University Press. This book was released on 2011-12-04 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern complex large-scale dynamical systems exist in virtually every aspect of science and engineering, and are associated with a wide variety of technological, environmental, and social phenomena. This book develops stability analysis and control design framework for nonlinear large-scale interconnected dynamical systems.

Author : Vasile Marinca
Publisher : Springer Science & Business Media
ISBN 13 : 3642227341
Total Pages : 403 pages
Book Rating : 4.49/5 ( download)

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Download or read book Nonlinear Dynamical Systems in Engineering written by Vasile Marinca and published by Springer Science & Business Media. This book was released on 2012-01-05 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents and extend different known methods to solve different types of strong nonlinearities encountered by engineering systems. A better knowledge of the classical methods presented in the first part lead to a better choice of the so-called “base functions”. These are absolutely necessary to obtain the auxiliary functions involved in the optimal approaches which are presented in the second part. Every chapter introduces a distinct approximate method applicable to nonlinear dynamical systems. Each approximate analytical approach is accompanied by representative examples related to nonlinear dynamical systems from to various fields of engineering.

Author : Jan A. Sanders
Publisher : Springer Science & Business Media
ISBN 13 : 1475745753
Total Pages : 259 pages
Book Rating : 4.57/5 ( download)

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Download or read book Averaging Methods in Nonlinear Dynamical Systems written by Jan A. Sanders and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book we have developed the asymptotic analysis of nonlinear dynamical systems. We have collected a large number of results, scattered throughout the literature and presented them in a way to illustrate both the underlying common theme, as well as the diversity of problems and solutions. While most of the results are known in the literature, we added new material which we hope will also be of interest to the specialists in this field. The basic theory is discussed in chapters two and three. Improved results are obtained in chapter four in the case of stable limit sets. In chapter five we treat averaging over several angles; here the theory is less standardized, and even in our simplified approach we encounter many open problems. Chapter six deals with the definition of normal form. After making the somewhat philosophical point as to what the right definition should look like, we derive the second order normal form in the Hamiltonian case, using the classical method of generating functions. In chapter seven we treat Hamiltonian systems. The resonances in two degrees of freedom are almost completely analyzed, while we give a survey of results obtained for three degrees of freedom systems. The appendices contain a mix of elementary results, expansions on the theory and research problems.